I don't know the exact starting date I started using my vehicle for work? what should I input?

If you know the general time frame of the month and year that you started using the vehicle for work, you should be fine to enter a date from that month. The main thing will be the tracking of your mileage for work, as well as total mileage for the vehicle (or beginning and ending odometer readings) for the year or since you started using the vehicle for work (if less than a year).